{
  "abstract": "We establish a universal scaling law for $α$-decay half-lives based on the variable $X_a = Z^a/\\sqrt{Q_α}$, which collapses experimental and theoretical data spanning over twenty orders of magnitude onto a single linear correlation. Global optimization over the complete set of even-even $α$ emitters reveals a uniquely sharp optimum at $a \\simeq 2/3$. This exponent is theoretically motivated by the leading geometric scaling of heavy nuclei and emerges quantitatively from the correlated nuclear systematics, driven by the correlated $(Z, Q_α)$ manifold of the nuclear chart. Strikingly, five structurally distinct semi-empirical models and an independent microscopic WKB calculation, when independently optimized with respect to the exponent $a$, yield values clustered around $2/3$, while the corresponding $a=2/3$ correlations remain highly linear without refitting the original model parameters. This emergent scaling law implies smooth variations of decay times along the heavy $r$-process path. We demonstrate analytically that, given a roughly uniform distribution of this variable, the scaling law naturally supports a quasi-power-law radioactive heating rate ($\\dotε \\propto t^{-1.24}$), consistent with full network calculations. Furthermore, integrating these scaling predictions directly into nuclear source terms for radiative-diffusion models yields multimessenger observables that accurately reproduce the kilonova AT2017gfo associated with the gravitational-wave event GW170817, demonstrating that the $Z^{2/3}/\\sqrt{Q_α}$ scaling coordinate provides a robust tool for modeling the radioactive engines of neutron-star mergers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25162",
  "author_total": 3,
  "authors": [
    {
      "name": "Hisham Anwer"
    },
    {
      "name": "B. Salah"
    },
    {
      "name": "A. R. Abdulghany"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fgd6t0e9whqw0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25162",
  "fulltext_url": null,
  "id": "fgd6t0e9whqw0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25162",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.HE"
    ],
    [
      "arxiv",
      "nucl-th"
    ],
    [
      "openalex",
      "3106|Nuclear physics research studies"
    ]
  ],
  "openalex": "W7214116836",
  "pdf_url": "https://arxiv.org/pdf/2609.25162",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fgd6t0e9whqw0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.25162",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25162"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.HE",
      "subfield": "high-energy-astrophysics"
    },
    {
      "field": "physics",
      "origin": "arxiv:nucl-th",
      "subfield": "nuclear"
    }
  ],
  "title": "Universal $Z^{2/3}/\\sqrt{Q_α}$ Scaling Law in Alpha Decay from Nuclei to Neutron-Star Mergers",
  "title_text": "Universal Z^2/3/√(Q_α) Scaling Law in Alpha Decay from Nuclei to Neutron-Star Mergers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:39Z",
  "url": "https://research.draconitic.com/paper/fgd6t0e9whqw0",
  "venue": "arXiv",
  "versions": []
}